Summing Multiple Measures

Question: I have a multi-stage testing procedure using items drawn from a pre-calibrated item bank. Each stage gives each person a measure and standard error. Can I combine these measures to give each person an overall measure?

Answer: The most exact answer would be to use all of a person's responses to all stages to estimate a new measure - but this may not be practical. Typically the first-stage is a short, wide subtest. The later stages may be narrower, longer subtests. So raw score performance and measurement precision can vary greatly between the subtests. RMT 8:3 p. 376, suggests that a useful combined measure is obtained by standard error weighting the subtest measures:

If it is reasonable to think of all subtests as measuring this same fixed effect, then its standard error approximates 1 / sqrt( Σ ( 1 / SE _subtest ² ) ).

Summing multiple measures. J.M. Linacre … 17:2 p. 925

Rasch Publications
Rasch Measurement Transactions (free, online)	Rasch Measurement research papers (free, online)	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Applying the Rasch Model 3rd. Ed., Bond & Fox	Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters	Introduction to Rasch Measurement, E. Smith & R. Smith	Introduction to Many-Facet Rasch Measurement, Thomas Eckes	Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr.	Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Journal of Applied Measurement	Rasch models for measurement, David Andrich	Constructing Measures, Mark Wilson	Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish:	Análisis de Rasch para todos, Agustín Tristán		Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

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